Statistical inference for data science - A companion to the Coursera Statistical Inference Course

The ideal reader for this book will be quantitatively literate and has a basic understanding of statistical concepts and R programming. The book gives a rigorous treatment of the elementary concepts in statistical inference from a classical frequentist perspective. After reading this book and performing the exercises, the student will understand the basics of hypothesis testing, confidence intervals and probability. Table of Contents 4 About this book 7 About the picture on the cover 7 Introduction 8 Before beginning 8 Statistical inference defined 8 Summary notes 9 The goals of inference 10 The tools of the trade 10 Different thinking about probability leads to different styles of inference 10 Exercises 11 Probability 12 Where to get a more thorough treatment of probability 12 Kolmogorov's Three Rules 13 Consequences of The Three Rules 13 Random variables 14 Probability mass functions 16 Probability density functions 16 CDF and survival function 18 Quantiles 20 Exercises 21 Conditional probability 22 Conditional probability, motivation 22 Conditional probability, definition 22 Bayes' rule 23 Diagnostic Likelihood Ratios 25 Independence 26 IID random variables 27 Exercises 28 Expected values 29 The population mean for discrete random variables 29 The sample mean 29 Continuous random variables 34 Simulation experiments 36 Summary notes 37 Exercises 38 Variation 39 The variance 39 The sample variance 41 Simulation experiments 42 The standard error of the mean 43 Data example 46 Summary notes 47 Exercises 48 Some common distributions 50 The Bernoulli distribution 50 Binomial trials 50 The normal distribution 51 The Poisson distribution 54 Exercises 56 Asymptopia 58 Asymptotics 58 Limits of random variables 58 The Central Limit Theorem 60 CLT simulation experiments 61 Confidence intervals 64 Simulation of confidence intervals 66 Poisson interval 70 Summary notes 72 Exercises 72 t Confidence intervals 74 Small sample confidence intervals 74 Gosset's t distribution 74 The data 76 Independent group t confidence intervals 78 Confidence interval 78 Mistakenly treating the sleep data as grouped 79 Unequal variances 81 Summary notes 82 Exercises 83 Hypothesis testing 85 Hypothesis testing 85 Types of errors in hypothesis testing 86 Discussion relative to court cases 86 Building up a standard of evidence 86 General rules 88 Two sided tests 89 T test in R 89 Connections with confidence intervals 90 Two group intervals 90 Exact binomial test 91 Exercises 92 P-values 94 Introduction to P-values 94 What is a P-value? 94 The attained significance level 95 Binomial P-value example 95 Poisson example 96 Exercises 96 Power 98 Power 98 Question 100 Notes 101 T-test power 101 Exercises 102 The bootstrap and resampling 104 The bootstrap 104 The bootstrap principle 106 Group comparisons via permutation tests 109 Permutation tests 110 Variations on permutation testing 110 Permutation test B v C 110 Exercises 112